The General Position Problem on Kneser Graphs and on Some Graph Operations

A vertex subset S of a graph G is a general position set of G if no vertex of S lies on a geodesic between two other vertices of S. The cardinality of a largest general position set of G is the general position number (gp-number) gp(G) of G. The gp-number is determined for some families of Kneser graphs, in particular for K(n, 2), n ≥ 4, and K(n, 3), n ≥ 9. A sharp lower bound on the gp-number is proved for Cartesian products of graphs. The gp-number is also determined for joins of graphs, coronas over graphs, and line graphs of complete graphs.